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Simplifying -20x4 + -36x2 + 54 = 0 Reorder the terms: 54 + -36x2 + -20x4 = 0 Solving 54 + -36x2 + -20x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -18x2 + -10x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -18x2 + -10x4)' equal to zero and attempt to solve: Simplifying 27 + -18x2 + -10x4 = 0 Solving 27 + -18x2 + -10x4 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -2.7 + 1.8x2 + x4 = 0.0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + 1.8x2 + 2.7 + x4 = 0.0 + 2.7 Reorder the terms: -2.7 + 2.7 + 1.8x2 + x4 = 0.0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + 1.8x2 + x4 = 0.0 + 2.7 1.8x2 + x4 = 0.0 + 2.7 Combine like terms: 0.0 + 2.7 = 2.7 1.8x2 + x4 = 2.7 The x term is 1.8x2. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x2 + 0.81 + x4 = 2.7 + 0.81 Reorder the terms: 0.81 + 1.8x2 + x4 = 2.7 + 0.81 Combine like terms: 2.7 + 0.81 = 3.51 0.81 + 1.8x2 + x4 = 3.51 Factor a perfect square on the left side: (x2 + 0.9)(x2 + 0.9) = 3.51 Calculate the square root of the right side: 1.8734994 Break this problem into two subproblems by setting (x2 + 0.9) equal to 1.8734994 and -1.8734994.Subproblem 1
x2 + 0.9 = 1.8734994 Simplifying x2 + 0.9 = 1.8734994 Reorder the terms: 0.9 + x2 = 1.8734994 Solving 0.9 + x2 = 1.8734994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x2 = 1.8734994 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x2 = 1.8734994 + -0.9 x2 = 1.8734994 + -0.9 Combine like terms: 1.8734994 + -0.9 = 0.9734994 x2 = 0.9734994 Simplifying x2 = 0.9734994 Take the square root of each side: x = {-0.986660732, 0.986660732}Subproblem 2
x2 + 0.9 = -1.8734994 Simplifying x2 + 0.9 = -1.8734994 Reorder the terms: 0.9 + x2 = -1.8734994 Solving 0.9 + x2 = -1.8734994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x2 = -1.8734994 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x2 = -1.8734994 + -0.9 x2 = -1.8734994 + -0.9 Combine like terms: -1.8734994 + -0.9 = -2.7734994 x2 = -2.7734994 Simplifying x2 = -2.7734994 Reorder the terms: 2.7734994 + x2 = -2.7734994 + 2.7734994 Combine like terms: -2.7734994 + 2.7734994 = 0.0000000 2.7734994 + x2 = 0.0000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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